What is the answer to x^x=15 ?

The answer to x^x=15 is x=(ln(15))/(\W_{0)(ln(15))}

The solution is x=(ln(15))/(\W_{0)(ln(15))}

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x^x=15

x^{x} = 15

x = \frac{ln ( 15 )}{W _{0} ( ln ( 15 ) )}

Solution steps

x^{x} = 15

Prepare

x^{x} = 15

for Lambert form:

x e^{- \frac{l n ( 15 )}{x}} = 1

Rewrite the equation with

\frac{ln ( 15 )}{x} = u

and

x = \frac{ln ( 15 )}{u}

(\frac{ln ( 15 )}{u}) e^{- u} = 1

Rewrite

(\frac{ln ( 15 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = ln (15)

Solve

u e^{u} = ln (15) : u = W_{0} (ln (15))

Verify Solutions:

u = W_{0} (ln (15))

True

The solution is

u = W_{0} (ln (15))

Substitute back

u = \frac{ln ( 15 )}{x},

solve for

x

Solve

\frac{ln ( 15 )}{x} = W_{0} (ln (15)) : x = \frac{ln ( 15 )}{W _{0} ( ln ( 15 ) )}

x = \frac{ln ( 15 )}{W _{0} ( ln ( 15 ) )}

4^{x} - 2^{x + 2} - 32 = 0

2 e^{4 x} = 8

3^{2 x - 1} = 8^{x}

\frac{2 7 ^{- 4} 9}{8 1 ^{- 2}} = 3^{x}

2 5^{x} = 625

What is the answer to x^x=15 ?
The answer to x^x=15 is x=(ln(15))/(\W_{0)(ln(15))}
Solve for x: x^x=15
The solution is x=(ln(15))/(\W_{0)(ln(15))}